Beyond Memorization: Extending Reasoning Depth with Recurrence, Memory and Test-Time Compute Scaling

Ivan Rodkin, Daniil Orel, Konstantin Smirnov, Arman Bolatov, Bilal Elbouardi, Besher Hassan, Yuri Kuratov, Aydar Bulatov, Preslav Nakov, Timothy Baldwin, Artem Shelmanov, Mikhail Burtsev

Track: long paper (up to 10 pages)

Keywords: sequence models, reasoning, transformers, state-space models, recurrent models, recurrent transformers, adaptive computation time, computation expressivity, computational complexity, chain-of-thoughts, reinforcement learning

TL;DR: We investigate how training methods and model architecture influence multi-step reasoning performance within the cellular automata framework. We show that reasoning depth can be significantly extended with recurrence, memory and test-time compute.

Abstract: Reasoning is a core capability of large language models, yet how multi-step reasoning is learned and executed remains unclear. We study this in a controlled cellular-automata (1dCA) framework that excludes memorisation by using disjoint train/test rules. Models are trained on short state sequences, required to infer the hidden local rule, and then chain it for multiple future steps. We find that most neural architectures learn the rule and achieve high next-step accuracy, but performance drops sharply as the required number of steps increases. Increasing model depth is crucial, and extending effective depth via recurrence, memory, or test-time compute improves results but remains bounded. Complementing these controlled experiments, a natural-language proxy game shows that contemporary LLMs largely fail on the complex setting. Together, these results separate genuine rule induction from memorisation, quantify how difficulty scales with reasoning depth, and highlight the joint roles of architecture and training/inference procedures.

Anonymization: This submission has been anonymized for double-blind review via the removal of identifying information such as names, affiliations, and identifying URLs.

Presenter: ~Ivan_Rodkin2

Format: Yes, the presenting author will attend in person if this work is accepted to the workshop.

Funding: Yes, the presenting author of this submission falls under ICLR’s funding aims, and funding would significantly impact their ability to attend the workshop in person.

Submission Number: 34